409 research outputs found
Hardy-Carleman Type Inequalities for Dirac Operators
General Hardy-Carleman type inequalities for Dirac operators are proved. New
inequalities are derived involving particular traditionally used weight
functions. In particular, a version of the Agmon inequality and Treve type
inequalities are established. The case of a Dirac particle in a (potential)
magnetic field is also considered. The methods used are direct and based on
quadratic form techniques
Some sharp inequalities for integral operators with homogeneous kernel
One goal of this paper is to show that a big number of inequalities for functions in L-p(R+), p >= 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp
Array processing in cryoseismology: a comparison to network-based approaches at an Antarctic ice stream
Seismicity at glaciers, ice sheets, and ice shelves
provides observational constraint on a number of glaciologi-
cal processes. Detecting and locating this seismicity, specifi-
cally icequakes, is a necessary first step in studying processes
such as basal slip, crevassing, imaging ice fabric, and iceberg
calving, for example. Most glacier deployments to date use
conventional seismic networks, comprised of seismometers
distributed over the entire area of interest. However, smaller-
aperture seismic arrays can also be used, which are typically
sensitive to seismicity distal from the array footprint and re-
quire a smaller number of instruments. Here, we investigate
the potential of arrays and array-processing methods to de-
tect and locate subsurface microseismicity at glaciers, bench-
marking performance against conventional seismic-network-
based methods for an example at an Antarctic ice stream.
We also provide an array-processing recipe for body-wave
cryoseismology applications. Results from an array and a
network deployed at Rutford Ice Stream, Antarctica, show
that arrays and networks both have strengths and weaknesses.
Arrays can detect icequakes from further distances, whereas
networks outperform arrays in more comprehensive studies
of a particular process due to greater hypocentral constraint
within the network extent. We also gain new insights into
seismic behaviour at the Rutford Ice Stream. The array de-
tects basal icequakes in what was previously interpreted to
be an aseismic region of the bed, as well as new icequake
observations downstream and at the ice stream shear mar-
gins, where it would be challenging to deploy instruments.
Finally, we make some practical recommendations for future
array deployments at glaciers
On the existence of solutions to the relativistic Euler equations in 2 spacetime dimensions with a vacuum boundary
We prove the existence of a wide class of solutions to the isentropic
relativistic Euler equations in 2 spacetime dimensions with an equation of
state of the form that have a fluid vacuum boundary. Near the fluid
vacuum boundary, the sound speed for these solutions are monotonically
decreasing, approaching zero where the density vanishes. Moreover, the fluid
acceleration is finite and bounded away from zero as the fluid vacuum boundary
is approached. The existence results of this article also generalize in a
straightforward manner to equations of state of the form
with .Comment: A major revision of the second half of the pape
The Devastating 2022 M6.2 Afghanistan Earthquake: Challenges, Processes, and Implications
On June 21st, a Mw6.2 earthquake struck the Afghan-Pakistan-border-region, situated within the India-Asia collision. Thousand thirty-nine deaths were reported, making the earthquake the deadliest of 2022. We investigate the event\u27s rupture processes by combining seismological and geodetic observations, aiming to understand what made it that fatal. Our Interferometric Synthetic Aperture Radar-constrained slip-model and regional moment-tensor inversion, confirmed through field observations, reveal a sinistral rupture with maximum slip of 1.8 m at 5 km depth on a N20°E striking, sub-vertical fault. We suggest that not only external factors (event-time, building stock) but fault-specific factors made the event excessively destructive. Surface rupture was favored by the rock foliation, coinciding with the fault strike. The distribution of Peak-Ground-Velocity was governed by the sub-vertical fault. Maximum slip was large compared to other events globally and might have resulted in peak-frequencies coinciding with resonance-frequencies of the local buildings and demonstrates the devastating impact of moderate-size earthquakes
On the gravitational potential of modified Newtonian dynamics
Producción CientíficaThe mathematical structure of the Poisson equation of Modified Newtonian Dynamics
(MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev
space whose Orlicz function is related to Milgrom’s μ-function, where there exists
existence and uniqueness of weak solutions. Since these do not have in principle
much regularity, a further study is performed where the gravitational field is not
too large, where MOND is most relevant. In that case the field turns out to be
H¨older continuous. Quasilinear MOND is also analyzed
Seismic Noise Interferometry and Distributed Acoustic Sensing (DAS): Inverting for the Firn Layer S ‐Velocity Structure on Rutford Ice Stream, Antarctica
Firn densification profiles are an important parameter for ice-sheet mass balance and palaeoclimate studies. One conventional method of investigating firn profiles is using seismic refraction surveys, but these are difficult to upscale to large-area measurements. Distributed acoustic sensing (DAS) presents an opportunity for large-scale seismic measurements of firn with dense spatial sampling and easy deployment, especially when seismic noise is used. We study the feasibility of seismic noise interferometry (SI) on DAS data for characterizing the firn layer at the Rutford Ice Stream, West Antarctica. Dominant seismic energy appears to come from anthropogenic noise and shear-margin crevasses. The DAS cross-correlation interferometry yields noisy Rayleigh wave signals. To overcome this, we present two strategies for cross-correlations: (a) hybrid instruments—correlating a geophone with DAS, and (b) stacking of selected cross-correlation panels picked in the tau-p domain. These approaches are validated with results derived from an active survey. Using the retrieved Rayleigh wave dispersion curve, we inverted for a high-resolution 1D S-wave velocity profile down to a depth of 100 m. The profile shows a “kink” (velocity gradient inflection) at ∼12 m depth, resulting from a change of compaction mechanism. A triangular DAS array is used to investigate directional variation in velocity, which shows no evident variations thus suggesting a lack of azimuthal anisotropy in the firn. Our results demonstrate the potential of using DAS and SI to image the near-surface and present a new approach to derive S-velocity profiles from surface wave inversion in firn studies
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